re.erl does define the mp/0 type, but since there is no -export_type declaration (described in the docs here), it is not available to other modules. (See also this Github issue)
To make the type re:mp() available, you'd need to add -export_type there.
In fact, there is a pull request that does that. So most likely this will work correctly once Erlang/OTP 27 is released.
